TSTP Solution File: SEU675^2 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU675^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:43:17 EDT 2024
% Result : Theorem 19.70s 4.16s
% Output : Refutation 19.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 47 ( 11 unt; 16 typ; 3 def)
% Number of atoms : 119 ( 23 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 488 ( 34 ~; 21 |; 11 &; 408 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 83 ( 40 ^ 38 !; 5 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(func_def,definition,
( func
= ( ^ [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
& ! [D: $i] :
( ( in @ D @ A )
=> ( ex1 @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ).
thf(funcSet_type,type,
funcSet: $i > $i > $i ).
thf(funcSet_def,definition,
( funcSet
= ( ^ [A: $i,B: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) ) @ ( func @ A @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(1,conjecture,
( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C
@ ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
@ ^ [D: $i] :
( ( subset @ D @ ( cartprod @ A @ B ) )
& ! [E: $i] :
( ( in @ E @ A )
=> ? [F: $i] :
( ( in @ F
@ ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) )
& ( ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) )
= ( setadjoin @ F @ emptyset ) ) ) ) ) ) )
=> ( ( subset @ C @ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( in @ sk3
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ sk2 ) )
@ ^ [A: $i] :
( ( subset @ A @ ( cartprod @ sk1 @ sk2 ) )
& ! [B: $i] :
( ( in @ B @ sk1 )
=> ? [C: $i] :
( ( in @ C
@ ( dsetconstr @ sk2
@ ^ [D: $i] : ( in @ ( kpair @ B @ D ) @ A ) ) )
& ( ( dsetconstr @ sk2
@ ^ [D: $i] : ( in @ ( kpair @ B @ D ) @ A ) )
= ( setadjoin @ C @ emptyset ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk3
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ sk2 ) )
@ ^ [D: $i] :
( ( subset @ D @ ( cartprod @ sk1 @ sk2 ) )
& ! [E: $i] :
( ( in @ E @ sk1 )
=> ? [F: $i] :
( ( in @ F
@ ( dsetconstr @ sk2
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) )
& ( ( dsetconstr @ sk2
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) )
= ( setadjoin @ F @ emptyset ) ) ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(12,plain,
( ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
& ! [A: $i] :
( ( in @ A @ sk1 )
=> ? [B: $i] :
( ( in @ B
@ ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) ) )
& ( ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) )
= ( setadjoin @ B @ emptyset ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( powerset @ ( cartprod @ sk1 @ sk2 ) )),bind(B,$thf( ^ [D: $i] : ( ( subset @ D @ ( cartprod @ sk1 @ sk2 ) ) & ! [E: $i] : ( ( in @ E @ sk1 ) => ? [F: $i] : ( ( in @ F @ ( dsetconstr @ sk2 @ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) ) & ( ( dsetconstr @ sk2 @ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) = ( setadjoin @ F @ emptyset ) ) ) ) ) )),bind(C,$thf( sk3 ))]]) ).
thf(29,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) )
= ( setadjoin @ ( sk5 @ A ) @ emptyset ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(31,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) )
= ( setadjoin @ ( sk5 @ A ) @ emptyset ) )
| ~ ( in @ A @ sk1 ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(4,plain,
( ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ( in @ sk4 @ sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(30,plain,
subset @ sk3 @ ( cartprod @ sk1 @ sk2 ),
inference(cnf,[status(esa)],[12]) ).
thf(42,plain,
( ~ $true
| ( in @ sk4 @ sk1 ) ),
inference(rewrite,[status(thm)],[4,30]) ).
thf(43,plain,
in @ sk4 @ sk1,
inference(simp,[status(thm)],[42]) ).
thf(28,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( in @ ( sk5 @ A )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(414,plain,
! [A: $i] :
( ( in @ ( sk5 @ A )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) ) )
| ( ( in @ sk4 @ sk1 )
!= ( in @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[43,28]) ).
thf(415,plain,
( in @ ( sk5 @ sk4 )
@ ( dsetconstr @ sk2
@ ^ [A: $i] : ( in @ ( kpair @ sk4 @ A ) @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[414:[bind(A,$thf( sk4 ))]]) ).
thf(5,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) )
| ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(100,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(rewrite,[status(thm)],[9,30]) ).
thf(101,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(459,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ sk4 )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) )
!= ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[415,101]) ).
thf(460,plain,
( ( dsetconstr @ sk2
@ ^ [A: $i] : ( in @ ( kpair @ sk4 @ A ) @ sk3 ) )
!= ( setadjoin @ ( sk5 @ sk4 ) @ emptyset ) ),
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( sk5 @ sk4 ))]]) ).
thf(826,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( ( setadjoin @ ( sk5 @ A ) @ emptyset )
!= ( setadjoin @ ( sk5 @ sk4 ) @ emptyset ) )
| ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) )
!= ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,460]) ).
thf(827,plain,
( ~ ( in @ sk4 @ sk1 )
| ( ( setadjoin @ ( sk5 @ sk4 ) @ emptyset )
!= ( setadjoin @ ( sk5 @ sk4 ) @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( sk4 ))]]) ).
thf(962,plain,
~ ( in @ sk4 @ sk1 ),
inference(simp,[status(thm)],[827]) ).
thf(976,plain,
~ $true,
inference(rewrite,[status(thm)],[962,43]) ).
thf(977,plain,
$false,
inference(simp,[status(thm)],[976]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU675^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 15:56:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.92/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.03 % [INFO] Parsing done (119ms).
% 1.20/1.04 % [INFO] Running in sequential loop mode.
% 1.69/1.25 % [INFO] nitpick registered as external prover.
% 1.69/1.25 % [INFO] Scanning for conjecture ...
% 1.79/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.99/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.99/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.35 % [INFO] Type checking passed.
% 1.99/1.35 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 19.70/4.15 % [INFO] Killing All external provers ...
% 19.70/4.16 % Time passed: 3607ms (effective reasoning time: 3113ms)
% 19.70/4.16 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 19.70/4.16 % Axioms used in derivation (0):
% 19.70/4.16 % No. of inferences in proof: 28
% 19.70/4.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3607 ms resp. 3113 ms w/o parsing
% 19.85/4.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.85/4.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------